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| 1. |
SHOW THAT :- tan⁴∅ + tan²∅ = sec⁴∅ -sec²∅ |
| Answer» We have to show that tan4\xa0θ + tan2\xa0θ = sec4\xa0θ – sec2\xa0θ.Here, tan2\xa0θ or tan4\xa0θ can be converted into sec2\xa0θ.So, LHS = tan4θ + tan2θ= tan2\xa0θ (tan2 θ + 1)= (sec2\xa0θ – 1) · sec2\xa0θ [ because, tan2\xa0θ = sec2\xa0θ – 1 and tan2\xa0θ + 1 = sec2\xa0θ]= sec4\xa0θ – sec2\xa0θ= RHSHence, proved. | |